【文档说明】GeneralEquilibriumpricetaking1(伦敦经济学院高级.pptx，共(38)页，355.892 KB，由精品优选上传

转载请保留链接：https://www.ichengzhen.cn/view-323176.html

以下为本文档部分文字说明：

MicroeconomicsGeneralEquilibrium:pricetakingExcessDemandDecentralis-ationandTradeAmany-personeconomyRobinsonC

rusoe'sProblemExcessDemandDecentralis-ationandTradeRobinsonCrusoe'sProblemGeneralEquilibriumWhyprice

-taking?Amany-personeconomyOverview...Sofarwe'vefocusedoncompetitiveequilibriumanalysis.Butwhy?Whyconcentrateonequilibrium?Whyassumecompetitive

behaviour?Let'sstartbyhavinganotherlookattheexchangeeconomy.We'llredrawtheEdgeworthboxSomepuzzlesincompetitiveequilibriumanalysisGeneralequilibriumR

obinsonCrusoe’sproblemDecentrali-sationandTradeAmany-personEconomyWhyprice-taking?ExcessdemandThesolutionconceptPricesandtheCor

eThesolutionconceptAnexchangeeconomyPricesandtheCoreWhyprice-taking?DEOax2ax1aDEx1ax2ax1bObOaDEx2bx1bObWhatwouldIdooutofequili

brium?Andwhatwouldhedo?Let'slookattheinnerworkings...BuildinganEdgeworthboxx1aR1aR2ax2aOaThesituationfromAlf'spointofviewHowAlfrespondsasp1/p2

changes...x1aR1aR2ax2aOaAlf'soffercurveWhataboutBill?x1bR1bR2bx2bObThesituationfromhispointofview...asanAustralianx1bR1bR2bx2bObHowBillrespondsas

p1/p2changes...x1bR1bR2bx2bObBill'soffercurveThetwooffercurvesx2bObx1ax2aOax1bR1bR1aR2aR2bOffersareonlyconsi

stentwherecurvesintersectBut,byconstruction...ThisisthecompetitiveequilibriumSatisfiesmaterialsbalanceEDequilibriumher

eendowmentherePrice-takingutility-maximisingBillendowmenthereequilibriumherePrice-takingutility-maximisingAlf•Butwhycompetitivebehaviour?•Wh

yshouldAlfandBillbehavethatway?•Wheredothepricescomefrom?Givencompetitivebehaviour,theCEistheonly"consistent"allocationsubjecttohhSpixiMi=1U(x)ma

xnhhSpixiMSowheredothepricescomefrom?WeneedamoregeneralsolutionconceptThenexaminehowprice-takingequilibriumrelatestothis.Let'sdevelopth

eapproachfortheexchangeeconomy,thoughitcouldapplytomoreinterestingeconomies.AfreshapproachGeneralequilibriumRobinsonCrusoe’sproblem

Decentrali-sationandTradeAmany-personEconomyWhyprice-taking?ExcessdemandThesolutionconceptPricesandtheCoreAnexchangeeconomyPricesan

dtheCoreAnexchangeeconomyWhyprice-taking?Viewthepopulation...Q2Q1...asnseparateindividualsQ0Acoalition...Thecoalitionconceptgivesu

sanimportantclue....isformedbyanysubgroupwe'vegotourendowmentswithusOnedayyoutakeyourbundlealongtothe"swapshop"......andsomebossype

rsonistherewhoproposes(insistson?)aparticularfeasibleallocation.Youandsomeothersdon'tlikethexbundley

ouwouldgetunderthisallocation......andyoufindthatbyusingjusttheresourcesyouallownyoucouldallgetautilitylevelatleastashighasthatofferedtoyouunderth

eproposedallocation.Youguysthereforerefusetoacceptit.Theideaofblocking:alittlestoryAnallocationisblocked...Q2^xb^xc^x

d^xa^xe^xf^xg^xl^xk...whichcandobetterforitselfifwecanfindacoalition...AproposedallocationforthewholeeconomyhhU(x)^hhU(x)...andthatarefe

asibleQ{1,2,...,nh}^h[x]isblockedbyQ"hQ,">"forsomehhQhSxhSRhQAcoalitionBundlesthatarepreferredbymembersofthecoalition...^h[x]Aforma

lapproachTheCoreisthesetofunblocked,feasibleallocationsUsetheideaofblockingtointroduceabasicsolutionconcept{Alf&Bill}{Alf}{Bill}Ina2-pe

rsonworldthereareveryfewcoalitionspossibleUsetheEdgeworthbox...x2bObx1ax2aOax1b...togetthecontractcurve{Alf}

blockstheseallocations...D{Bill}blockstheseallocations...{Alf,Bill}(together)blockthese...EndowmentNo-onecanblockanallocationhereThe2-pe

rsoncoreGeneralequilibriumRobinsonCrusoe’sproblemDecentrali-sationandTradeAmany-personEconomyWhyprice-taking?ExcessdemandThesolutionco

nceptPricesandtheCoreAnexchangeeconomyThesolutionconceptAnexchangeeconomyWhyprice-taking?x2bObx1ax2aOax1bDEThecompe

titiveequilibriumagainx2bObx1ax2aOax1bDEAnycompetitiveequilibriummustlieinthecoreEveryCEallocationmustbelongtothecoreOfcourseitispossiblethatnoC

Eexists(seenextlecture)ButwhatofothercoreallocationswhicharenotCE?Let'stakeaclose-uplookAsimpleresultDBAlfBillAlfBillATheextre

mesofthe2-personcoreCoreCEIntroducingAlfandBill'slong-losttwinbrothers...Rememberwearedealingwitha2-personmodelButwilltherealwaysbenon-CEpoin

tsinthecore?Abasicrelation...AlfandhistwinbrotherArthurhavethesamepreferencesandendowmentsLikewiseth

etwinsBillandBenNowofcoursetherearemorepossibilitiesofformingcoalitionsSolet'sclonetheeconomy{Arthur&

Ben}{Arthur}{Ben}{Alf&Arthur}{etc,etc}{Bill&Ben}{Alf&Bill}{Alf}{Bill}{Alf,Arthur&Bill}...plussomenewonesAlltheoldcoaliti

onsarepossible...Willthesestillbecoreallocationsinthe4-personeconomy?BAAlf'n'ArthurBill'n'BenAlf'n'ArthurBill'n'BenDAlf,Arthur,BenBillG...leavingt

heBentwinoutsidethecoalitionThisallocationisnotasolution...ButitshowsthatthecorehasbecomesmallerNo.{Alf-Arthur-Bill}canblockA...Alf½[xa

+Ra](G)Arthur½[xa+Ra](G)Billxb(A)BenRb(D)2Ra+RbThecoalitionFeasibleHowtheblockingcoalitionworksABDCanthisallocationbeblocked?AnA-

personwouldbebetteroffsomewherehereBingo!Whatiftherewere500ofeachtype...?500oftheAtribe450oftheBtribe500oftheAtribe400oftheBtr

ibe500oftheAtribe360oftheBtribe500oftheAtribe310oftheBtribe500oftheAtribe250oftheBtribeIfNisbiggertheremaybemorebl

ockingcoalitionsABDETheonlyallocationleftinthe2N-personcore(eventually)...Asyouclonetheeconomythecorebecomessm

aller.Inthelimititcontainsonlycompetitiveequilibriumallocations.ButnoticethatthisrequiresbalancedreplicationoftheAlfandBilltribesA

nditassumesthatallthesevariouscoalitionsaresomehowrelevantApowerfulresult:theshrinkingcoreEndowmentsPreferencesAllo

cationsCoalitionsBlockingAnswertoquestion:whyprice-taking?Inalargeeconomywithsuitablysmallagents.......it'stheonlythingtodo.Afinal

reminder:Basicconceptsofthecore•Aggregatingfirms•Aggregatingconsumers•WARP•Propertiesofdemandsystems•TheSeparationTheorem•Firm#4

slides18-26•Consumer#4slides39-44•Consumer#1slides23.24•Consumer#3slides5,6•GenEqm#2slides14-20,24,25.